How do you solve for the inverse of the following polynomial function?
f(x)= 1000x^3 - 600x^2 + 120x. I need it step by step because I'm really confused. Thanks for your help!
1. Examine the function to get critical ppints and (if it exists) the point of inflection.
2. I've found a point of inflection with a horizontal tangent at $\displaystyle W\left(\frac15\ ,\ 8\right)$
Therefore
- the function is increasing monotically and must have an increasing inverse function.
- the function can be re-written as
$\displaystyle f(x)=y= a \cdot \left(x-\frac15 \right)^3+8$
Expand this term and compare it with original term of the function. You'll get a = 1000.
3. Swap the x and y variables in the equation of the function to get the inverse:
$\displaystyle x=1000 \cdot \left(y-\frac15\right)^3+8$
Solve for y. I've got:
$\displaystyle f^{-1}(x)=y=\frac15 - \frac1{10} \cdot \sqrt[3]{x-8}$